Taking lessons from countries that have outstripped the UK in numeracy, it has moved away from independent learning within an integrated theme-based day back to a teacher-led approach with dedicated subject time.
Primary 1 at Gilmerton, one of the pilot schools, shows what happens in practice. In one of three slots a week timetabled for maths, pupils were formed into groups - large enough to qualify as a "class" but differentiated sufficiently in ability between a more and a less able (or "focus") group.
Instructing one of the groups to sit around her, class teacher Mags Logan asked each pupil to call out a number in a sequence up to five. It sounds easy, but if you don't listen to your classmates, you lose the place. First lesson learnt: counting means concentration.
Minds on the job, the pupils counted aloud up to five as they touched and moved objects around, placing them according to totals in and out of cups. No inaccuracy was allowed to pass uncorrected. Then, as if it was a big adventure, Ms Logan asked them to move cardboard cut-out cars around the plan of a car park.
Every task completed won fulsome praise from teacher and fellow pupils who were encouraged to clap. Recap and recall - at the end of a highly intensive three-quarters of an hour the children had learnt important skills.
The delight was clear in their faces. Ms Logan says: "As their counting develops so does their self-esteem and confidence. They are getting a real feel for numbers."
Her five-year-olds were indeed at the start of a great adventure. Writing and recording kept to a minimum, they were encouraged to sharpen mental agility and to have a dialogue with maths. Number facts and skills were constantly reinforced by verbal responses within games, rhymes and chants.
After working through the pilot materials their numeracy skills should be far beyond what is recommended in the 5-14 guidelines, achieving level A by the end of their second year. Six-year-olds could be mentally adding and subtracting numbers up to 20.
The pilot programme, started last autumn, has been backed by pound;125,000 from the New Deal budget, which has made possible the appointment of a part-time nursery nurse in each pilot school, plus two full-time development officers and the production of teaching resources and detailed plans for every lesson in the programme.
The move into maths follows Edinburgh's pioneering early intervention in literacy five years ago. When the New Deal money finishes in April the council will look to the Scottish Office's Excellence Fund to enable 36 schools to run both the maths and literacy programmes in an extended pilot.
Looking ahead to when all 103 city primaries might benefit, Steve MacEachainn, one of the development officers, says that even without extra support progress is registered. "The important factor is the input of direct teaching."
Early intervention in maths is essential, Mr MacEachainn says. "If children do not acquire basic maths skills in the early years they are unlikely to make up lost ground later on in school."